Questions tagged [open-quantum-systems]

The study of open quantum systems is concerned with understanding and predicting the dynamics of quantum systems that are coupled significantly to their surroundings, leading to effects such as dissipation and decoherence.

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Correspondence between ground state and steady state in quantum systems

An open quantum system $S$ is usually studied by considering a system of interest effectively interacting with an environment $E$. The environment is treated effectively because of the difficulty of ...
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Lindblad equation for heisenberg operators?

Very related to this question: Is it possible to go from the Master Equation formalism to Heisenberg-Langevin equations I don't yet have enough reputation to comment so I'm asking the new question ...
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Derive master equation if one Lindblad term is already given

I have a following question: is it possible to derive master equation with Open Quantum systems approach if one Lindblad term is already given? For example, assume we have Liouville equation given ...
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Derivation of Correlation function in Open Quantum Systems and Master Equation

I have a question and I have searched a long time about it without any success. It is about how to include convolution broadening incorrelation functions of bath operators, when using Open Quantum ...
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How to determine the collapse operator for a Lindblad equation

Given a Hamiltonian $H$, how can I relate the collapse operator for the Lindblad equation to a given environmental effect? Also, how can I relate the constant $\gamma$ in front of the sum of the ...
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How do I show the separability of this density matrix?

I am stuck since a longer time regarding this exercise where I need to work with a density matrix of the given form $$\displaystyle \rho_{AB}(X)= \frac{1}{N+\text{tr}X^2}\left( {\begin{array}{cc} ...
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Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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Spin-Boson coupling

Typically while coupling a single spin to a bunch of bosons (Harmonic oscillators) a $\sigma_x$ or $\sigma_z$ coupling operator is chosen for the system operator coupled to the position of the bosons, ...
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Example of an infinite volume Lindblad system

What is an explicit example of a Lindbladian \begin{align*} L(\rho) = - i \lbrack H_A, \rho \rbrack + G \sum_{j} V_j \rho V_j^* - \frac{1}{2}(V_j^* V_j \rho + \rho V_j^* V_j) \end{align*} acting on ...
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Solving linear Lindblad equations in the Heisenberg picture?

I'm interested in solving the explicit time dependence of operators in a simple open system described by a Lindblad equation. The concrete example I'm interested in is a harmonic oscillator with the ...
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Noise add to the Lindblad equation or Liouville-Von Neumann equation

I am working on an open system and I would like to use the Lindblad master equation but also I would like to add noise to it. If is possible. All the books and papers I did read about tells me that ...
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How to find the Heisenberg picture from the master equation without Lindblad structure?

My question is closely related to this post and this one too. I understand that with a Lindbladian type master equation, it is possible to find the differential equation for an observable. However, my ...
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What is the characteristics time scale of a quantum system, in context of the Markovian approximation?

In the theory of open quantum system, we make the markovian approximation when the timescale of the memory of the reservoir is small. But this timescale is measured with respect to the characteristic ...
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Super-ohmic bosonic bath correlation function

In quantum Brownian motion, bosonic/harmonic oscillator bath and interaction described by Hamiltonian $$ H_B = \sum_{n}\hbar\omega_n(b_n^\dagger b_n) \\ H_I = -\sigma_x \otimes B $$ and $$ B = \sum_n \...
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Describing small, NRQM systems purely in terms of photons

Is there a canonical way to describe an open, non-relativistic quantum system with density matrix $\rho(t)$ entirely in terms of the light that it emits and absorbs (and vice versa?) Or is it possible ...
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Solving the Lindblad quantum master equation in matrix form

I have just started learning density matrix and quantum master equations, and I am given a problem set that asks to find the solution to the Lindblad equation with $H$, $L_+$, $L_-$, $L_z$, and $\rho(...
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Lindblad and Input-Output Formalism in Quantum Optics

I'm confused about how to apply the Lindblad formalism and the input-output formalism in practice, and how one goes between the two. Suppose I have a cavity (C) coupled to a reservoir (R), with the ...
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Going from stochastic Schrödinger equation to master equation

I am currently reading the book "Quantum measurement and control" by Wiseman and Milburn (https://www.amazon.ca/Quantum-Measurement-Control-Howard-Wiseman/dp/1107424151) and something is really ...
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Lindblad from infinitesimal Kraus sum representation

I have a few basic queries regarding a proof in the set of notes MIT: Open Quantum Systems, the following is stated: We can derive the Lindblad equation from an infinitesimal evolution described by ...
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154 views

Why does the Redfield equation model thermal relaxation while the Lindblad equation does not?

In open quantum systems, we model a process known as thermal relaxation. What is this process, and why is it that only the Redfield equation models this process, and the Lindblad equation doesn't?
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Expectation Values in the Quantum Trajectory Formalism

If I want to know the expectation value of an operator O in the quantum trajectory formalism, I average over $N$ trajectories, where I call one such trajectory $\Psi_n$: \begin{equation} \langle O \...
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Is the establishment of entanglement inevitable with the passage of time?

Derivation of the Lindblad master equation starts with the assumption that at an initial time $t=0$, the total density matrix is the product of the density matrices of the system $\rho_S$ and that of ...
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Can quantum systems interact with multiple environments of different types?

If it can, how can we write the Hamiltonian of the total System is it just (for example with N bath) $$ H_{tot} = H_{s} + H_{B_{1}} + H_{B_{2}} + ... + H_{B_{N}} + H_{I_{1}} + H_{I_{2}} + ... +H_{I_{N}...
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Eigenvalues of generators [closed]

If I have a hamiltonian like $\omega\sigma_z$ and 2 Lindblad operators as $\gamma\sigma_-$ and $\gamma\sigma_+$ how can I find eigenvalues of generators? I think I should put the general form of $\rho$...
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How can we “isolate” a qubit

From Wikipedia : In ion quantum computer, if the ions are not properly isolated, noise can result from ions interacting with external electromagnetic fields, which creates random movement and destroys ...
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Semi-group in quantum open systems

In the literature of Open Quantum System, one often comes across the following ($t_2>t_1,>0$): Semi-group property of a map: $A(t_1+t_2,0) = A(t_2,0) A(t_1,0)$. What does this mean physically,...
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Can an arbitrary quantum system of finite size be made to reliably relax to its ground state? Is there a physical principle prohibiting this?

I am talking about the possibility of reliably cooling an arbitrary quantum system of FINITE size (for example, localized on earth), to its ground state through any means, like exposure to a special ...
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Why are there so few ion-trap experiments studying quantum trajectories?

The quantum trajectory theory describes the behaviour of a quantum system under continuous monitoring. Initially it is theoretically studied in quantum optics and single atom scenario (e.g., ion trap ...
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Time-evolution operator written through a commutator [duplicate]

I found this expression for the time-evolution operator: $$\begin{split} U(t) & = T_{\leftarrow}\exp\left[-i\int_0^t ds H(s)\right] \\ &= \exp\left[-\frac{1}{2}\int_0^t ds\int_0^t ds' [H(s),H(...
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Fluctuation dissipation theorems in dynamic processes: a comparison

I do not understand what the first and the second fluctuation- dissipation theorems physically represent and what are the differences between the first and the second on the physical side. As a ...
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In the theory of open quantum systems, what is really meant by *information backflow* from the environment to the system?

In the context of an Open Quantum System (OQS) i.e. a quantum system coupled to a quantum environment, what is really meant by information backflow from the environment to the system? I'm newly ...
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Projecting Density Matrix into Edge States Subspace

I'm reading and trying to understand the paper by Diehl, S., Rico, E., Baranov, M. et al. "Topology by dissipation in atomic quantum wires". Nature Phys 7, 971–977 (2011). https://doi.org/10....
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In what sense is a quantum damped harmonic oscillator dissipative?

The classical Hamiltonian of a damped harmonic oscillator $$H=\frac{p^2}{2m}e^{-\gamma t}+\frac{1}{2}m\omega^2e^{\gamma t}x^2,~(\gamma>0)\tag{1}$$ when promoted to quantum version, remains ...
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Why are simple models of coupled pendulums incapable of describing irreversible energy dissipation?

Consider two pendulums $A$ and $B$ coupled by a spring and also regard $A+B$ to be a completely isolated system. Let us start the system in an initial configuration where only one of the pendulums (...
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Lindblad equation solution

I have been trying to solve a Lindblad Equation and then thought about whether there is a closed form Lindblad Equation solution for most types. Googling hasn't lead me to anything useful. So, is ...
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Transformation to rotating frame

I want to apply a transformation to the rotating frame of a two level system such that a state in the transformed frame is $ |\hat{\phi} \rangle = U |\phi \rangle$, where U is the generator of ...
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Density operator of a system $S$ coupled to a bath $B$

In the second equation of section 8.1 in this MIT OCW lecture notes, I can't understand how they went from $$\rho_{S}(t)=Tr_{B}\{\rho_{SB}(t)\}=\sum_{k}\langle k|U_{SB}(\rho_{S}(0)\otimes|0\rangle\...
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Finding density matrix of open system with nearest-neighbor hopping interactions

I want to find the density matrix of the system for an open system with nearest-neighbor hopping interactions using a hamiltonian in the interaction picture. I know that I have to solve a master ...
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What is an example of a system with non-vanishing topological entanglement entropy at finite temperatures?

In this paper: https://doi.org/10.1088/1367-2630/14/3/033044 it is show that for Kitaev toric code looses topological entanglement entropy over long times if it is thermally opened. What is an example ...
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Green's functions in the Keldysh-formalism and quantum stochastic calculus

Introduction The Keldysh path integral can be thought of as a reformulation of the quantum optical master equation, which describes the markovian time evolution of the density operator of an open ...
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Green Function in Open Quantum Systems

Imagine an open quantum system interacting with an environment that admits a density matrix (Markovian) description in terms of Lindbladians ($c$ and $c^\dagger$). Is there a meaningful way to define ...
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The master equation and continuous measurements

To derive the master equation under a continuous measurement we first define the two measurement operators $$M_0=\mathbb{I}-\left(R~/~2+iH\right)dt \tag 1$$ $$M_1=c\sqrt{dt}, \tag 2 $$ where $M_0$ ...
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Time evolution of a tripartite quantum state

Question: How do we write the unitary evolution of a tripartite system in Hilbert Space $\mathcal{H}_A \otimes \mathcal{H}_B \otimes \mathcal{H}_C$ when it is subject to two unitary evolution ...
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Markov Approximation and Master Equation Derivation

In deriving the master equation, I am coming across the Markov Approximation which says: Suppose environment $E$ and system $S$ interact and exchange some energy with each other. Then $E$ would ...
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Lindblad superoperator and generated dynamics

In quantum mechanics, in order to evolve the state of an open system, I can use an equation like this $\dot\rho(t)=\mathcal{L}\rho(t)$, where $\mathcal{L}$ is the Lindblad superoperator. In general, $\...
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How to efficiently check if a superoperator is Lindbladian?

Superoperators are linear maps on the vector space of linear operator. The Lindbladian superoperators are the important subset that can be expressed in the form $$\mathcal{L}[\rho] = -i (H \rho - \rho ...
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Clarifications needed on why certain arguments related to quantum maps dubbed as false [closed]

As I was learning more about the evolution of open quantum systems, I came across this question. Reading through the answers, I found this paper by A. Shaji and E.C.G. Sudarshan. The mathematical ...
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How can one model quantum walks in photosynthesis?

I have been working on quantum biology and found something interesting that I would like to write an equation for. Scientists have wondered how plants have such a high efficiency in photosynthesis; ...
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Caldeira-Leggett Dissipation: frequency shift due to bath coupling

I am trying to understand the Caldeira-Leggett model. It considers the Lagrangian $$L = \frac{1}{2} \left(\dot{Q}^2 - \left(\Omega^2-\Delta \Omega^2\right)Q^2\right) - Q \sum_{i} f_iq_i + \sum_{i}\...
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Computation of wavefunction after small time evolution [closed]

I have to simulate the wavefunction of a quantum driven duffing oscillator coupled to a bath of harmonic oscillators. The master equation is given by $\frac{d\rho}{dt}=\frac{i}{\hbar}[\rho,H_{sys}]-\...